I can see a potential problem brewing, if LW's son calls the FIL "Grandpa" but calls SMIL simply by her name; LW says His father is “Grandpa” to his new wife’s grandchildren.

Unless SMIL has the same name as LW's deceased MIL, I can't see why SMIL can't be called "Grandma (SMIL's Name)" to distinguish from "Grandma (MIL's name)." That's what we did with our kids' paternal step-grandmother and paternal grandmother who died when the kids were very young. I wonder if there is friction between LW's husband and SMIL that's not mentioned in the letter.